Subgroups — C₃×#733×C₉₇ #37555747

Order 23571.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²×C₉₇	C₃	1	3	yes	maximal
2	C₃²×C₉×C₉₇	C₃	1	1	yes	maximal, characteristic
3	#733×C₉₇	C₃	1	9	yes	maximal, direct product factor
4	C₃³×C₉₇	C₃²	1	1	yes	characteristic
5	3₋¹⁺²×C₉₇	—	3	6	no	—
6	3₋¹⁺²×C₉₇	C₃²	1	9	yes	—
7	C₃×C₉×C₉₇	—	3	2	no	—
8	C₃×C₉×C₉₇	—	3	1	no	—
9	C₃×C₉×C₉₇	—	3	3	no	—
10	C₃×C₉×C₉₇	C₃²	1	3	yes	—
11	C₃²×C₉₇	—	3	3	no	—
12	C₃²×C₉₇	H(3,𝔽₃)	1	2	yes	—
13	C₃²×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃²×C₉₇	C₃³	1	1	yes	characteristic
15	C₉×C₉₇	—	3	3	no	—
16	C₉×C₉₇	—	3	9	no	—
17	C₃×C₉₇	—	3	2	no	—
18	C₃×C₉₇	—	3	1	no	—
19	C₃×C₉₇	#733	1	3	yes	direct product factor
20	C₃×C₉₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×#733	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₉₇	C₃×#733	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×3₋¹⁺²	C₃×C₉₇	1	3	yes	—
24	C₃²×C₉	C₃×C₉₇	1	1	yes	characteristic
25	#733	C₃×C₉₇	1	9	yes	direct product factor
26	C₃³	C₃²×C₉₇	1	1	yes	characteristic
27	3₋¹⁺²	—	3	6	no	—
28	3₋¹⁺²	C₃²×C₉₇	1	9	yes	—
29	C₃×C₉	—	3	2	no	—
30	C₃×C₉	—	3	1	no	—
31	C₃×C₉	—	3	3	no	—
32	C₃×C₉	C₃²×C₉₇	1	3	yes	—
33	C₃²	—	3	3	no	—
34	C₃²	H(3,𝔽₃)×C₉₇	1	2	yes	—
35	C₃²	H(3,𝔽₃)×C₉₇	1	1	yes	characteristic
36	C₃²	C₃³×C₉₇	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	3	9	no	—
39	C₃	—	3	2	no	—
40	C₃	—	3	1	no	—
41	C₃	#733×C₉₇	1	3	yes	direct product factor
42	C₃	C₃×H(3,𝔽₃)×C₉₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₉₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃³×C₉₇
prime radical	C₃³×C₉₇	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉₇ ◁ C₃³×C₉₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #733×C₉₇	C₃	direct (N × H)
19. C₃×C₉₇	#733	direct (N × H)
21. C₃×#733	C₉₇	direct (N × H)
22. C₉₇	C₃×#733	direct (N × H)
25. #733	C₃×C₉₇	direct (N × H)
41. C₃	#733×C₉₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×3₋¹⁺²×C₉₇	3
C₃²×C₉×C₉₇	3
#733×C₉₇	3
C₃×#733	97

Subgroups — C3×#733×C97 #37555747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#733×C₉₇ #37555747